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SUBROUTINE DLARHS( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS,
$ A, LDA, X, LDX, B, LDB, ISEED, INFO )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* February 29, 1992
*
* .. Scalar Arguments ..
CHARACTER TRANS, UPLO, XTYPE
CHARACTER*3 PATH
INTEGER INFO, KL, KU, LDA, LDB, LDX, M, N, NRHS
* ..
* .. Array Arguments ..
INTEGER ISEED( 4 )
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
* Purpose
* =======
*
* DLARHS chooses a set of NRHS random solution vectors and sets
* up the right hand sides for the linear system
* op( A ) * X = B,
* where op( A ) may be A or A' (transpose of A).
*
* Arguments
* =========
*
* PATH (input) CHARACTER*3
* The type of the real matrix A. PATH may be given in any
* combination of upper and lower case. Valid types include
* xGE: General m x n matrix
* xGB: General banded matrix
* xPO: Symmetric positive definite, 2-D storage
* xPP: Symmetric positive definite packed
* xPB: Symmetric positive definite banded
* xSY: Symmetric indefinite, 2-D storage
* xSP: Symmetric indefinite packed
* xSB: Symmetric indefinite banded
* xTR: Triangular
* xTP: Triangular packed
* xTB: Triangular banded
* xQR: General m x n matrix
* xLQ: General m x n matrix
* xQL: General m x n matrix
* xRQ: General m x n matrix
* where the leading character indicates the precision.
*
* XTYPE (input) CHARACTER*1
* Specifies how the exact solution X will be determined:
* = 'N': New solution; generate a random X.
* = 'C': Computed; use value of X on entry.
*
* UPLO (input) CHARACTER*1
* Specifies whether the upper or lower triangular part of the
* matrix A is stored, if A is symmetric.
* = 'U': Upper triangular
* = 'L': Lower triangular
*
* TRANS (input) CHARACTER*1
* Specifies the operation applied to the matrix A.
* = 'N': System is A * x = b
* = 'T': System is A'* x = b
* = 'C': System is A'* x = b
*
* M (input) INTEGER
* The number or rows of the matrix A. M >= 0.
*
* N (input) INTEGER
* The number of columns of the matrix A. N >= 0.
*
* KL (input) INTEGER
* Used only if A is a band matrix; specifies the number of
* subdiagonals of A if A is a general band matrix or if A is
* symmetric or triangular and UPLO = 'L'; specifies the number
* of superdiagonals of A if A is symmetric or triangular and
* UPLO = 'U'. 0 <= KL <= M-1.
*
* KU (input) INTEGER
* Used only if A is a general band matrix or if A is
* triangular.
*
* If PATH = xGB, specifies the number of superdiagonals of A,
* and 0 <= KU <= N-1.
*
* If PATH = xTR, xTP, or xTB, specifies whether or not the
* matrix has unit diagonal:
* = 1: matrix has non-unit diagonal (default)
* = 2: matrix has unit diagonal
*
* NRHS (input) INTEGER
* The number of right hand side vectors in the system A*X = B.
*
* A (input) DOUBLE PRECISION array, dimension (LDA,N)
* The test matrix whose type is given by PATH.
*
* LDA (input) INTEGER
* The leading dimension of the array A.
* If PATH = xGB, LDA >= KL+KU+1.
* If PATH = xPB, xSB, xHB, or xTB, LDA >= KL+1.
* Otherwise, LDA >= max(1,M).
*
* X (input or output) DOUBLE PRECISION array, dimension(LDX,NRHS)
* On entry, if XTYPE = 'C' (for 'Computed'), then X contains
* the exact solution to the system of linear equations.
* On exit, if XTYPE = 'N' (for 'New'), then X is initialized
* with random values.
*
* LDX (input) INTEGER
* The leading dimension of the array X. If TRANS = 'N',
* LDX >= max(1,N); if TRANS = 'T', LDX >= max(1,M).
*
* B (output) DOUBLE PRECISION array, dimension (LDB,NRHS)
* The right hand side vector(s) for the system of equations,
* computed from B = op(A) * X, where op(A) is determined by
* TRANS.
*
* LDB (input) INTEGER
* The leading dimension of the array B. If TRANS = 'N',
* LDB >= max(1,M); if TRANS = 'T', LDB >= max(1,N).
*
* ISEED (input/output) INTEGER array, dimension (4)
* The seed vector for the random number generator (used in
* DLATMS). Modified on exit.
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL BAND, GEN, NOTRAN, QRS, SYM, TRAN, TRI
CHARACTER C1, DIAG
CHARACTER*2 C2
INTEGER J, MB, NX
* ..
* .. External Functions ..
LOGICAL LSAME, LSAMEN
EXTERNAL LSAME, LSAMEN
* ..
* .. External Subroutines ..
EXTERNAL DGBMV, DGEMM, DLACPY, DLARNV, DSBMV, DSPMV,
$ DSYMM, DTBMV, DTPMV, DTRMM, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
C1 = PATH( 1: 1 )
C2 = PATH( 2: 3 )
TRAN = LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' )
NOTRAN = .NOT.TRAN
GEN = LSAME( PATH( 2: 2 ), 'G' )
QRS = LSAME( PATH( 2: 2 ), 'Q' ) .OR. LSAME( PATH( 3: 3 ), 'Q' )
SYM = LSAME( PATH( 2: 2 ), 'P' ) .OR. LSAME( PATH( 2: 2 ), 'S' )
TRI = LSAME( PATH( 2: 2 ), 'T' )
BAND = LSAME( PATH( 3: 3 ), 'B' )
IF( .NOT.LSAME( C1, 'Double precision' ) ) THEN
INFO = -1
ELSE IF( .NOT.( LSAME( XTYPE, 'N' ) .OR. LSAME( XTYPE, 'C' ) ) )
$ THEN
INFO = -2
ELSE IF( ( SYM .OR. TRI ) .AND. .NOT.
$ ( LSAME( UPLO, 'U' ) .OR. LSAME( UPLO, 'L' ) ) ) THEN
INFO = -3
ELSE IF( ( GEN .OR. QRS ) .AND. .NOT.
$ ( TRAN .OR. LSAME( TRANS, 'N' ) ) ) THEN
INFO = -4
ELSE IF( M.LT.0 ) THEN
INFO = -5
ELSE IF( N.LT.0 ) THEN
INFO = -6
ELSE IF( BAND .AND. KL.LT.0 ) THEN
INFO = -7
ELSE IF( BAND .AND. KU.LT.0 ) THEN
INFO = -8
ELSE IF( NRHS.LT.0 ) THEN
INFO = -9
ELSE IF( ( .NOT.BAND .AND. LDA.LT.MAX( 1, M ) ) .OR.
$ ( BAND .AND. ( SYM .OR. TRI ) .AND. LDA.LT.KL+1 ) .OR.
$ ( BAND .AND. GEN .AND. LDA.LT.KL+KU+1 ) ) THEN
INFO = -11
ELSE IF( ( NOTRAN .AND. LDX.LT.MAX( 1, N ) ) .OR.
$ ( TRAN .AND. LDX.LT.MAX( 1, M ) ) ) THEN
INFO = -13
ELSE IF( ( NOTRAN .AND. LDB.LT.MAX( 1, M ) ) .OR.
$ ( TRAN .AND. LDB.LT.MAX( 1, N ) ) ) THEN
INFO = -15
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DLARHS', -INFO )
RETURN
END IF
*
* Initialize X to NRHS random vectors unless XTYPE = 'C'.
*
IF( TRAN ) THEN
NX = M
MB = N
ELSE
NX = N
MB = M
END IF
IF( .NOT.LSAME( XTYPE, 'C' ) ) THEN
DO 10 J = 1, NRHS
CALL DLARNV( 2, ISEED, N, X( 1, J ) )
10 CONTINUE
END IF
*
* Multiply X by op( A ) using an appropriate
* matrix multiply routine.
*
IF( LSAMEN( 2, C2, 'GE' ) .OR. LSAMEN( 2, C2, 'QR' ) .OR.
$ LSAMEN( 2, C2, 'LQ' ) .OR. LSAMEN( 2, C2, 'QL' ) .OR.
$ LSAMEN( 2, C2, 'RQ' ) ) THEN
*
* General matrix
*
CALL DGEMM( TRANS, 'N', MB, NRHS, NX, ONE, A, LDA, X, LDX,
$ ZERO, B, LDB )
*
ELSE IF( LSAMEN( 2, C2, 'PO' ) .OR. LSAMEN( 2, C2, 'SY' ) ) THEN
*
* Symmetric matrix, 2-D storage
*
CALL DSYMM( 'Left', UPLO, N, NRHS, ONE, A, LDA, X, LDX, ZERO,
$ B, LDB )
*
ELSE IF( LSAMEN( 2, C2, 'GB' ) ) THEN
*
* General matrix, band storage
*
DO 20 J = 1, NRHS
CALL DGBMV( TRANS, MB, NX, KL, KU, ONE, A, LDA, X( 1, J ),
$ 1, ZERO, B( 1, J ), 1 )
20 CONTINUE
*
ELSE IF( LSAMEN( 2, C2, 'PB' ) ) THEN
*
* Symmetric matrix, band storage
*
DO 30 J = 1, NRHS
CALL DSBMV( UPLO, N, KL, ONE, A, LDA, X( 1, J ), 1, ZERO,
$ B( 1, J ), 1 )
30 CONTINUE
*
ELSE IF( LSAMEN( 2, C2, 'PP' ) .OR. LSAMEN( 2, C2, 'SP' ) ) THEN
*
* Symmetric matrix, packed storage
*
DO 40 J = 1, NRHS
CALL DSPMV( UPLO, N, ONE, A, X( 1, J ), 1, ZERO, B( 1, J ),
$ 1 )
40 CONTINUE
*
ELSE IF( LSAMEN( 2, C2, 'TR' ) ) THEN
*
* Triangular matrix. Note that for triangular matrices,
* KU = 1 => non-unit triangular
* KU = 2 => unit triangular
*
CALL DLACPY( 'Full', N, NRHS, X, LDX, B, LDB )
IF( KU.EQ.2 ) THEN
DIAG = 'U'
ELSE
DIAG = 'N'
END IF
CALL DTRMM( 'Left', UPLO, TRANS, DIAG, N, NRHS, ONE, A, LDA, B,
$ LDB )
*
ELSE IF( LSAMEN( 2, C2, 'TP' ) ) THEN
*
* Triangular matrix, packed storage
*
CALL DLACPY( 'Full', N, NRHS, X, LDX, B, LDB )
IF( KU.EQ.2 ) THEN
DIAG = 'U'
ELSE
DIAG = 'N'
END IF
DO 50 J = 1, NRHS
CALL DTPMV( UPLO, TRANS, DIAG, N, A, B( 1, J ), 1 )
50 CONTINUE
*
ELSE IF( LSAMEN( 2, C2, 'TB' ) ) THEN
*
* Triangular matrix, banded storage
*
CALL DLACPY( 'Full', N, NRHS, X, LDX, B, LDB )
IF( KU.EQ.2 ) THEN
DIAG = 'U'
ELSE
DIAG = 'N'
END IF
DO 60 J = 1, NRHS
CALL DTBMV( UPLO, TRANS, DIAG, N, KL, A, LDA, B( 1, J ), 1 )
60 CONTINUE
*
ELSE
*
* If PATH is none of the above, return with an error code.
*
INFO = -1
CALL XERBLA( 'DLARHS', -INFO )
END IF
*
RETURN
*
* End of DLARHS
*
END
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